Probing an additional bottom Yukawa coupling via $bg\to bA\to bZH$ signature

The recent discovery of the bottom quark Yukawa coupling ($hbb$) of the 125 GeV scalar motivates one to search for extra bottom Yukawa coupling that may exist in the nature. The two Higgs doublet model without a discrete $Z_2$ symmetry allows the possibility of additional bottom Yukawa coupling ${\rho }_{bb}$. We show that ${\rho }_{bb}$ can be searched directly at the LHC via $bg\to bA\to bZH$ and $gg\to b\bar{b}A\to b\bar{b}ZH$ processes, where $A$ and $H$ are the CP-odd and CP-even scalars respectively. We find that the $bg\to bA\to bZH$ process could be discovered with $\sim 300$ fb${}^{-1}$ integrated luminosity if $m_A\sim 300$ GeV, while the latter process may emerge in the high luminosity LHC (HL-LHC) data. A discovery might touch upon the parameter space required for the electroweak baryogenesis.